A high pressure center is where the pressure
has been measured to be
the highest relative to its surroundings. That means, moving in any
direction away from the "High" will result in a decrease in pressure.
A high pressure center also represents the center of an anticyclone
and is indicated on a weather map by a blue "H".

Winds flow clockwise
around a high pressure center in the northern hemisphere, while in the southern
hemisphere, winds flow
counterclockwise around a high.

Sinking air in the vicinity of a high pressure center suppresses
the upward motions needed to support the
development of clouds and precipitation.
This is why fair weather
is commonly associated with an area of high pressure.